If the area of a rectangle is only 26.88% of the area of the square constructed on the diagonal, find the ratio of the length and breadth of the rectangle.

Sure, let's solve this step by step.

Step 1: Let's denote the length of the rectangle as 'l' and the breadth as 'b'. The diagonal of the rectangle is √(l² + b²).

Step 2: The area of the square constructed on the diagonal of the rectangle is (l² + b²).

Step 3: According to the problem, the area of the rectangle is 26.88% of the area of the square constructed on the diagonal. So, lb = 0.2688(l² + b²).

Step 4: Rearrange the equation to find the ratio of length to breadth. Divide both sides of the equation by b*l, we get 1 = 0.2688 * ((l²/b) + (b²/b)).

Step 5: Simplify the equation, we get 1 = 0.2688 * (l/b + 1).

Step 6: Subtract 1 from both sides, we get 0 = 0.2688 * (l/b) - (1 - 0.2688).

Step 7: Solve for l/b, we get l/b = (1 - 0.2688) / 0.2688.

Step 8: Calculate the value, we get l/b = 2.72.

So, the ratio of the length to the breadth of the rectangle is 2.72:1.